Socrates: ... if [a person] were a philosopher of the eristic and contentious sort, I should say to him: You have my answer, and if I am wrong, your business is to take up the argument and refute me. But if we were friends, and were talking as you and I are now, I ought of course to reply in a milder strain and more in the dialectician's vein; that is to say, I should not only speak the truth, but I should make use of premises which the person interrogated would be willing to admit. And this is the way in which I shall endeavour to approach you.

If you want to debate, fine. Socrates wasn't trying to convince anyone of anything (in this context). It is true that at the start of the text I took the above quote from, Meno of Thessaly asked of Socrates a question, in which to have an answer. Socrates answered that he did not know, and asked Meno if he knew. Meno eventually admits he does not know. They then proceed to decide on what exactly they do not know. That is the heart of the Socratic method, working together towards better understanding.

In terms of teaching, as wharfinger has taken it, it is a method for being sure that the student knows (or learns) what the teacher knows. It is asking to hear what the teacher knows in the student's words. As wharfinger touches on, it is a good way to discuss matters of mind and of process. As we see on "Who Wants to Be A Millionaire", it helps to talk it out. However, in this way, the teacher must either have a firm grasp of the material examined (such as wharfinger's computer science professor), or not care where the discussion ends up (more towards Socrates' situation). Unless the whole is known, the discussion can end up far from the intended end.

As a side note, sockpuppet's description of Protarchus' headache from use is somewhat typical of the Dialogues. Meno describes Socrates as a torpedo fish, one that torpifies and confuses. Socrates goes on to quiz one of Meno's slaves in geometry, both instructing him (through questions, not giving answers) and confusing him (by virtue of the same method).